73. Three hundred thousand five hundred. 74. Six million one hundred thousand. 75. Four million four thousand and forty-nine. 76. Seventeen million one hundred and twenty-five. 77. One billion, one million, one thousand and one. 78. Five hundred and twenty-one billion, three hundred million, three hundred thousand and one. 79. Five trillion, five billion, five million, five thousand and five hundred and fifty-five. 80. Six quadrillion, six hundred million, four hundred and fiftynine thousand and sixteen. 81. Two hundred and fifty quintillion, six quadrillion, two billion, three hundred and forty thousand.† Figures on the slate are written thus,― 1 2 3 4 5 6 7 8 9 0 SIMPLE ADDITION.' XI. 1. Add together 9 dollars, 7 dollars, 5 dollars, 8 dollars, 6 dollars, 4 dollars, and 3 dollars, thus; (1.) (2.) (3.) (4.) (5.) (6.) 9 dollars. 8 tons. 3 cents. 8 ounces. 5 mills. 8 hats. XI. Q. How much is 33 and 9? What is the 42 called? See 7. + Remarks to the Learner. As very high numbers are somewhat difficult to apprehend; it may not be amiss to illustrate, by a few examples the value of the words milion, billion, trillion, and quadrillion, according to the English notation. Suppose that a person employed in telling money, reckons a hundred pieces in a minute, and continues to do so twelve hours each day, he will take nearly fourteen days to reckon a million. A thousand men would take more than 38 years to reckon a billion. The inhabitants of the United States in 1820, were about 10 million. Now if we sup pose all these persons had been constantly employed in counting money since the birth of Christ, they could not as yet have reckoned a trillion. Though we admit the earth, from the creation, to have been as populous as it is at present (being about 800 million,) and the whole human race to have been counting money without intermission; they could scarcely, as yet, have reckoned the five hun dredth part of a quadrillion of pieces. 1 ADDITION, L. additio.] Any thing added; adding; joining; uniting two or more numbers in one sum. * (1). A. 42 dollars. (2). A. 42 tons. (3.) A 45 cents. (4.) A 52 ounces. (5.) A 46 mills. (6.) A. 54 hats. 7. The Answer in adding is called the sum or amount. 8. A drover bought 5 cows at one time, 8 at another, 9 at another.. How many cows did he buy in all? 5 cows. 8 cows. 9 cows. A. 22 cows. 17 cows. P. 22 cows. PROOF. Having added upwards as before; which makes 22, draw a line under the 5 at top; then add downwards all the figures under the 5, thus, 8 and 9 are 17; Then if the 17 and the 5 at top make 22, as they do, the work is right. In like manner perform and prove the following examples. (13.) 8 7 pence oxen. 8 calves. 9 shillings. 5 pence 14. Since 1 ten and 1 unit, for instance, make neither 2 tens, nor 2 units, (although 1 and 1 are 2); but 1 ten, which is 10 units, added to 1 unit will make 11 units, thus keeping the 1 ten in its proper place, therefore : 15. Write units under units, tens under tens, hundreds under hundreds, &c., then add each column separately. 20. Ciphers are passed over in‹dding, because they are used to fill 25. A man bought a farm for 4,000 dollars; he paid for his cows 405 dollars; for his horses 320 dollars; for his farming utensils 60 Q. What do I ten and 1 unit make added together? See 14. Why not 2 tens or 2 units? How then should units, tens, &c., be written and added? 15. How pr ciphers to be regarded in adding? 20 dollars; and his expenses for securing his title were 3 dollars. What was the amount of the whole? A. 4,788 dollars. 26. Add into one sum forty, two hundred, three hundred and nineteen, and nine hundred and forty. A. 1499. 27. What is the amount of one thousand, thirty-three thousand three hundred and sixty-one, five hundred thousand and ten, five million and five thousand? A. 5,539,371. 28. What is the sum of five, fifty, five hundred, five thousand, fifty thousand, five hundred thousand, five million, fifty million, five hundred million, and five billion? A. Ten 5s. 29. Add together 8 trillion, 800 billion, 80 billion, 8 billion, 800 million, 80 million, 8 million, 800 thousand, 80 thousand, 8 thousand, 8 hundred, 80 and 8. A. Thirteen 8s. 30. Find the sum of 3 trillion, 3 billion, 3 million, 3 thousand and 3; 20 billion, 20 million, 20,020; 200 million; 200 thousand and 200; 16 million, 16 thousand and 16. A. 3,023.239,239,239. 31. What is the amount of 4 million and six, 300 thousand two hundred, 90 thousand three hundred and one, 4 thousand two hundred and ten, 1 hundred and 70, eleven and 1? A. 4,394,899. 32. A cashier has in one drawer 5,305 dollars, in another 406 dollars, in another 7,312, in another 2,309, and in another 42. What amount has he in all the drawers? 5305 406 7312 4 2 A. 1 5 3 74 The first column makes 24 units or 2 tens and 4 units; write down only the 4 units and add in the 2 tens with the column of tens, which is called carrying 1 for every ten. The 2 to carry to 4 tens makes 6 and 1 are 7 tens, and none to earry. The next column makes 13 hundreds, or 1 thousand and 3 hun dreds; carry the 1 thousand to the thousands; therefore ; 33. When the amount of any single column is 10 or more :- -Write down only the right hand figure, and carry the left hand figure or figures to the next column. 38. From the above it appears that we begin on the right and carry 1 for every 10; because figures increase from the right to the left in a tenfold proportion. Q. When, in adding several columns, the right-hand column makes 24, for instance: what is to be done with it? 32. What is this process called? 32. What is the direction for carrying? 33. What is the reason for beginning and arrying in this manner? 38. How many do you carry when the sum is 59? 115? 39. Add together 28,992; 21,995; 24,834 and 5,148. A. 80,969. 40. A man bought a suit of clothes for 57 dollars, a pair of boots for 8 dollars, and a secretary for 28 dollars. What is the amount of the whole? A. 93 dollars. 41. In an orchard, 20 trees bear pears, 54 bear peaches, and 6 bear plums. How many trees are there in the orchard? A. 80 trees. 42. A man bought a barrel of flour for 10 dollars, a barrel of molasses for 29 dollars, and a barrel of pork for 19 dollars. What did the whole cost him? A. 58 dollars. 43. What is the sum of eighty-seven, two hundred and seventeen, eight thousand nine hundred and eighty-six, and nine? A. 9,299. 44. Find the sum of eight thousand and twenty, four hundred and seventy-nine, thirty thousand and sixty-five. A. 38,564. 45. General George Washington was born A. D.1 1732, and lived 67 years. In what year did he die? RECAPITULATION. A. 1799. 46. ADDITION is the uniting of two or more numbers in one number, which is called their sUM or AMOUNT. 47. Simple AdDITION is the adding of numbers of the same denomination. RULE. 48. Write the numbers in columns, so that units may be added to units, tens to tens, hundreds to hundreds, &c. 49. Begin on the right and place underneath each column its whole amount, unless it be 10 or more; in which case set down the right-hand figure only, and carry the left-hand one to the next column 50. Do the same with each column to the last, under which write the whole sum. 51. PROOF. Omit the top line, and find the sum of all the rest, adding downwards; if the numbers were before added upwards and vice versa. Then if this amount added to the top line, corresponds with the first amount, the work is supposed to be right. 52. Or, more practically, add the figures downwards without omitting the top line, and if the two amounts agree they will probably be right. 53. The rule as well as the proof is based3 on the well krown axiom,* that the whole is equal to the sum of all its parts. Q. What is Addition? 46. Simple Addition? 47. Rule? 48, 49, 50. What are the two methods of proof? 51. 52. What is the reason for both? 53. 1 A. D. The A. stands for anno, L. for year; and D. for Domini, L. of our Lord. Hence Anno Domini means, in the year of our Lord; and A. D. 1732 means so many years since Christ, or our Saviour came on earth. 2 VICE VERSA. That is, upwards if the figures were before added downwards. Generally vice versa, from the Latin, means the terms being exchanged; thus, the generous should be rich and vice versa, that is, the rich should be generous. 3 BASED, [L. basis, foundation.] Founded; reduced in value. 4 AXIOM, [G. axioma.] A self-evident truth; that which is so plain, that no proof can make it any plainer 60. A father gave to his oldest son 4,200 dollars, to his second 2,300 dollars, and to his youngest 1,560 dollars. What is the amount of these several sums? (61.) 987654321 987 6 5 4 3 2 8 7 6 5 4 3 A. 8,060 dollars. 63. Find the sum of 1 billion, 97 million, 393 thousand, 686, and 1 quadrillion 324 trillion, 198 billion, 879 million, 148 thousand, and A. 1,324,199,976,541,739. 53. 64. A gentleman purchased a ship for 25,000 dollars, and sold it for 3,715 dollars more than it cost him. What did he get for it? A. 28,715 dollars. 65. A gentleman sold a tract of wild land which was 1.750 dollars less than it cost him. for it? 66. A merchant had a store-house in which he had at one time 6,000 bushels of corn, 5,756 bushels of wheat, 1,375 bushels of rye, 8,750 bushels of oats, and had room enough left for 2,000 bushels more of corn. How many bushels would the store-house hold? A. 23,881 bushels. 67. Two men started from New York and traveled in opposite directions. The one was to go 37 miles a day, and the other 35 miles. How far would they be apart the first night? A. 72 miles. 68. How far were they apart the 2d night! 69. How far were they apart the 3d night? 70. How far were they apart the 4th night? 71. How far were they apart the 5th night? 72. How far were they apart the 6th night? A. 144 miles. |